JEE Mains · Physics · STD 11 - 2. motion in straight line

A car travels a distance of \(x\) with speed \(v_1\) and then same distance \(x\) with speed \(v_2\) in the same direction. The average speed of the car is

A \(\frac{ v _1 v _2}{2\left( v _1+ v _2\right)}\)
B \(\frac{v_1+v_2}{2}\)
C \(\frac{2 x }{ v _1+ v _2}\)
D \(\frac{2 v _1 v _2}{ v _1+ v _2}\)

Verified Solution

Answer & Solution

Correct Answer

(D) \(\frac{2 v _1 v _2}{ v _1+ v _2}\)

Step-by-step Solution

Detailed explanation

\(\text { Average velocity }=\frac{\text { Total displacement }}{\text { Total time }}\) \(=\frac{ x + x }{\frac{ x }{ v _1}+\frac{ x }{ v _2}}=\frac{2 v _1 v _2}{ v _1+ v _2}\)

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

Same subject

List - I	List - II
A. Boltzmann constant	I. \([M^{-1}L^3T^{-2}]\)
B. Stefan's constant	II. \([ML^2T^{-1}]\)
C. Planck's constant	III. \([ML^2T^{-2}K^{-1}]\)
D. Gravitational constant	IV. \([ML^0T^{-3}K^{-4}]\)

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